The present invention relates to a multi-stage pressure apparatus ideally suited for creating pressure and vacuum conditions in a bi-directional pneumatic conveyance system such as the one generally disclosed in U.S. Pat. No. 5,562,367, the disclosure of which is incorporated herein in its entirety. More particularly, the present invention relates to a multi-stage pressure apparatus including independently operable pressure generation units and internal chambers and valve mechanisms to selectively create pressure or vacuum conditions in response to mere activation of the pressure generation units. The present invention also relates to a method of pressure or vacuum generation with such a multi-stage apparatus, and an actual bi-directional pneumatic conveyance system incorporating such an apparatus.